The dynamics of radiative, near-limit, stretched premixed flames was investigated analytically and numerically, with emphasis on pulsating stability for sub-unity Lewis numbers. The analysis includes both flame stretch and order-unity heat loss, and yields a dispersion equation for the stability of radiative stretched flames subjected to symmetrical and asymmetrical perturbations. The dispersion equation reduces to that of the classical thermo-diffusional stability analysis of Sivashinsky in the limit of small heat loss, small stretch rate, and infinite flame separation distance. Results show that sub-limit flames are stable near both radiation and stretch extinction limits, and that oscillation occurs only at moderate flame stretch rates. The unstable regime and the stability diagram were obtained. Numerical simulation with detailed chemical kinetics and transport models yielded results that are in good agreement with theory. The present work also provides a satisfactory explanation of the experimental results obtained in microgravity.